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Comparison functions and fixed point results in partial metric spaces. (English) Zbl 1242.54023
Summary: The aim of this article is to clearly formulate various possible assumptions for a comparison function in contractive conditions and to deduce respective (common) fixed point results in partial metric spaces. Since standard metric spaces are special cases, these results also apply for them. We will show by examples that there exist situations when a partial metric result can be applied, while the standard metric one cannot.

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] S. G. Matthews, “Partial metric topology,” in Proceedings of the 8th Summer Conference on General Topology and Applications, pp. 183-197, The New York Academy of Sciences, 1994. · Zbl 0911.54025
[2] I. Altun and K. Sadarangani, “Corrigendum to “Generalized contractions on partial metric spaces” [Topology and Its Applications vol. 157, pp. 2778-2785, 2010] [MR2729337],” Topology and Its Applications, vol. 158, no. 13, pp. 1738-1740, 2011. · Zbl 1207.54052 · doi:10.1016/j.topol.2011.05.023
[3] I. Altun, F. Sola, and H. Simsek, “Generalized contractions on partial metric spaces,” Topology and Its Applications, vol. 157, no. 18, pp. 2778-2785, 2010. · Zbl 1207.54052 · doi:10.1016/j.topol.2010.08.017
[4] L. Ćirić, B. Samet, H. Aydi, and C. Vetro, “Common fixed points of generalized contractions on partial metric spaces and an application,” Applied Mathematics and Computation, vol. 218, no. 6, pp. 2398-2406, 2011. · Zbl 1244.54090 · doi:10.1016/j.amc.2011.07.005
[5] D. {\Dj}ukić, Z. Kadelburg, and S. Radenović, “Fixed points of geraghty-type mappings in various generalized metric spaces,” Abstract and Applied Analysis, vol. 2011, Article ID 561245, 13 pages, 2011. · Zbl 1231.54030 · doi:10.1155/2011/561245
[6] R. Heckmann, “Approximation of metric spaces by partial metric spaces,” Applied Categorical Structures, vol. 7, no. 1-2, pp. 71-83, 1999. · Zbl 0993.54029 · doi:10.1023/A:1008684018933
[7] D. Ilić, V. Pavlović, and V. Rako\vcević, “Some new extensions of Banach’s contraction principle to partial metric space,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1326-1330, 2011. · Zbl 1292.54025 · doi:10.1016/j.aml.2011.02.025
[8] S. Romaguera, “Fixed point theorems for generalized contractions on partial metric spaces,” Topology and Its Applications, vol. 159, no. 1, pp. 194-199, 2012. · Zbl 1232.54039 · doi:10.1016/j.topol.2011.08.026
[9] S. Oltra and O. Valero, “Banach’s fixed point theorem for partial metric spaces,” Rendiconti dell’Istituto di Matematica dell’Università di Trieste, vol. 36, no. 1-2, pp. 17-26, 2004. · Zbl 1080.54030
[10] W. Shatanawi, B. Samet, and M. Abbas, “Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces,” Mathematical and Computer Modelling, vol. 55, pp. 680-687, 2012. · Zbl 1255.54027
[11] O. Valero, “On Banach fixed point theorems for partial metric spaces,” Applied General Topology, vol. 6, no. 2, pp. 229-240, 2005. · Zbl 1087.54020
[12] D. W. Boyd and J. S. W. Wong, “On nonlinear contractions,” Proceedings of the American Mathematical Society, vol. 20, pp. 458-464, 1969. · Zbl 0175.44903 · doi:10.2307/2035677
[13] J. Matkowski, “Fixed point theorems for mappings with a contractive iterate at a point,” Proceedings of the American Mathematical Society, vol. 62, no. 2, pp. 344-348, 1977. · Zbl 0349.54032 · doi:10.2307/2041041
[14] S. Radenović, Z. Kadelburg, D. Jandrlić, and A. Jandrlić, “Some results on weak contraction maps,” Bulletin of the Iranian Mathematical Society. In press. · Zbl 06283455
[15] B. Fisher, “Four mappings with a common fixed point,” The Journal of the University of Kuwait, vol. 8, pp. 131-139, 1981. · Zbl 0472.54030
[16] A. Meir and E. Keeler, “A theorem on contraction mappings,” Journal of Mathematical Analysis and Applications, vol. 28, pp. 326-329, 1969. · Zbl 0194.44904 · doi:10.1016/0022-247X(69)90031-6